# American Institute of Mathematical Sciences

July  2017, 13(3): 1189-1211. doi: 10.3934/jimo.2016068

## A multi-objective approach for weapon selection and planning problems in dynamic environments

 1 College of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, China 2 Business School, Hunan University, Changsha 410082, Hunan, China 3 State Key Laboratory of Complex System Simulation, Beijing Institute of System Engineering, Beijing, China 4 College of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, China

* Corresponding author

Received  July 2015 Published  October 2016

Fund Project: The authors are supported by National Natural Science Foundation of China under Grants 71501181, 71401167, 71201169 and 71371067.

This paper addresses weapon selection and planning problems (WSPPs), which can be considered as an amalgamation of project portfolio and project scheduling problems. A multi-objective optimization model is proposed for WSPPs. The objectives include net present value (NPV) and effectiveness. To obtain the Pareto optimal set, a multi-objective evolutionary algorithm is presented for the problem. The basic procedure of NSGA-Ⅱ is employed. The problem-specific chromosome representation and decoding procedure, as well as genetic operators are redesigned for WSPPs. The dynamic nature of the planning environment is taken into account. Dynamic changes are modeled as the occurrences of countermeasures of specific weapon types. An adaptation process is proposed to tackle dynamic changes. Furthermore, we propose a flexibility measure to indicate a solution's ability to adapt in the presence of changes. The experimental results and analysis of a hypothetical case study are presented in this research.

Citation: Jian Xiong, Zhongbao Zhou, Ke Tian, Tianjun Liao, Jianmai Shi. A multi-objective approach for weapon selection and planning problems in dynamic environments. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1189-1211. doi: 10.3934/jimo.2016068
##### References:

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##### References:
Chromosome representation
A conceptual example of the adaptation process
A conceptual example of the recovery process
The whole adaptation procedure for each solution after dynamic changes occur
Non-dominated set obtained with mutation rate 0.5 and crossover rates varying from 0.6 to 1.0
Non-dominated sets obtained with crossover rate 0.7 and mutation rates varying from 0.1 to 0.6
Convergence graph using hypervolume measure over time in 30 runs
Comparison between non-dominated sets with and without the consideration of synergy effectiveness
Behavior of the non-dominated set in the presence of dynamic changes
Solutions in the presence of 1-4 dynamic changes without and after adaptation
Solutions in the presence of 5-8 dynamic changes without and after adaptation
A conceptual example of the calculation of adaptation effectiveness
Parameters of different type of weapons in the synthetical case
 $w$ $a^{low}_{w}$ $a^{up}_{w}$ $c_w$ $d_w$ $r_w$ 1 15 40 3 6 0 2 10 30 4 8 0 3 6 20 10 10 0 4 5 10 12 15 0 5 12 20 5 7 0 6 8 16 8 8 0 7 8 18 9 8 0 8 6 15 10 5 0 9 5 15 13 11 0 10 4 8 18 14 0 11 4 8 15 20 0 12 4 16 8 9 0 13 5 12 18 15 0 14 4 10 16 16 0 15 6 18 14 12 0 16 8 20 12 14 0 17 3 8 18 22 0 18 5 10 16 18 0 19 3 9 20 18 0 20 7 15 5 10 0
 $w$ $a^{low}_{w}$ $a^{up}_{w}$ $c_w$ $d_w$ $r_w$ 1 15 40 3 6 0 2 10 30 4 8 0 3 6 20 10 10 0 4 5 10 12 15 0 5 12 20 5 7 0 6 8 16 8 8 0 7 8 18 9 8 0 8 6 15 10 5 0 9 5 15 13 11 0 10 4 8 18 14 0 11 4 8 15 20 0 12 4 16 8 9 0 13 5 12 18 15 0 14 4 10 16 16 0 15 6 18 14 12 0 16 8 20 12 14 0 17 3 8 18 22 0 18 5 10 16 18 0 19 3 9 20 18 0 20 7 15 5 10 0
Parameters of dynamic environments
 $No.$ 1 2 3 4 5 6 7 8 $w$ 10 4 20 2 17 5 6 12 $t\_CW_w$ 22 26 28 30 35 48 50 54
 $No.$ 1 2 3 4 5 6 7 8 $w$ 10 4 20 2 17 5 6 12 $t\_CW_w$ 22 26 28 30 35 48 50 54
Correlation analysis between flexibility and adaptation in the presence of 8 changes
 $No.$ 1 2 3 4 5 6 7 8 $corrcoef$ 0.8559 0.7892 0.5409 0.3797 0.3233 0.8663 0.7933 0.4643 $P-value$ 0 0 0 0 0 0 0 0
 $No.$ 1 2 3 4 5 6 7 8 $corrcoef$ 0.8559 0.7892 0.5409 0.3797 0.3233 0.8663 0.7933 0.4643 $P-value$ 0 0 0 0 0 0 0 0
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